In a uniform electric field, a point charge of mass m and charge q is released from rest. If there are no other forces acting on the particle, then which of the following graphs, correctly show the dependence of the particles speed v on the distance x travelled by it? [Graphs are schematic and not drawn to scale]

Question

In a uniform electric field, a point charge of mass m and charge q is released from rest. If there are no other forces acting on the particle, then which of the following graphs, correctly show the dependence of the particles speed v on the distance x travelled by it? [Graphs are schematic and not drawn to scale] (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

Using work-energy theorem, qEx=(1/2)mv2 ⇒ v2=(2 q E/m)x⇒ v=√(2 q E/m)√x

Using work-energy theorem, qEx=21​mv2 ⇒v2=m2qE​x⇒v=m2qE​​x​

Using work-energy theorem,
$qE x = \frac{1}{2} m v^{2}$
$\Rightarrow v^{2} = \frac{2 qE}{m} x \Rightarrow v = \frac{2 qE}{m} x$